The time complexity of 1-limited automata is investigated from a descriptional complexity view point. Though the model recognizes regular languages only, it may use quadratic time in the input length. We show that, with a polynomial increase in size and preserving determinism, each 1-limited automaton can be transformed into an halting linear-time equivalent one. We also obtain polynomial transformations into related models, including weight-reducing Hennie machines, and we show exponential gaps for converse transformations in the deterministic case.